110 K.A. Kvåle et al. 14.2.2 Efficient Stabilization Analysis To determine if poles corresponding to analyses with different orders corresponds to the same mode, a modal indicator is used, which in the current study is the modal assurance criterion (MAC) number. The MAC number between poles p and q are computed as follows: MACp;q D jf qg Tf pgj 2 f qg Tf qg f pg Tf pg (14.17) where the N is the complex conjugate operator. The poles from the current order are identified to correspond to the poles from the previous order by finding the maximum value of the MAC between the poles in the different orders. The most common choice for a modal indicator is the frequency, but because the modes are closely spaced in frequency, the MAC number is a better choice for the current study. For a pole from a analysis with a higher order to be considered stable, it has to fulfill the following criteria when compared to a previous reference pole: it has to deviate a maximum amount in frequency and damping, and their mode shapes have to yield a MAC value above a certain threshold. To increase the clarity of the stabilization plots, the parameter stability level is introduced. For a stability level of s, the above requirements have to be fulfilled with all poles corresponding to calculations with 1-s orders lower than the queried pole. 14.3 The Bergsøysund Bridge The Bergsøysund Bridge is a pontoon bridge with total length 931 m and main span 845 m, located on the northwestern coast of Norway. It consists of a steel truss supported by seven concrete pontoons (Fig. 14.1). The bridge is arc-shaped to reduce the bending moments due to lateral wave forces. The bridge is only supported in the ends, as no side-mooring is present. An extensive monitoring system is currently operating on the bridge (Fig. 14.2). Three-dimensional anemometers are capturing winds 7 m above the deck level at locations spread across the deck, while wave radars are monitoring the sea surface elevation near the center of the bridge. Furthermore, the response of the bridge is measured by means of two triaxial accelerometers on each pontoon and a single Global Navigation Satelite Systems (GNSS) displacement sensor located at midspan on top of the deck. The reader is referred to Kvåle et al. [10] for a more in-detail description of the monitoring system. Fig. 14.1 The Bergsøysund Bridge. Photograph by NTNU/K. A. Kvåle
RkJQdWJsaXNoZXIy MTMzNzEzMQ==